A Unified Approach to Reliability, Availability, Performability Analysis Based on Markov Processes with Rewards

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Valentina S. Viktorova

Nikolai V. Lubkov

Armen S. Stepanyants

Abstract

This paper discusses a unified approach to reliability, availability and performability analysis of complex engineering systems. Theoretical basis of this approach is continuous-time discrete state Markov processes with rewards. From reliability modeling point of view complex systems are the systems with static and dynamic redundancy, imperfect fault coverage, various recovery strategies, multilevel operation and varying severity of failure states. We propose a unified method of calculating the reliability, availability and performability indices based on the definition of special forms of reward matrix. This method proved to be effective in calculating both cumulative and instantaneous measures in steady-state and transient cases. We describe special analytical software which implements suggested method. We demonstrate the flexibility of the proposed method and software by analyzing multilevel process unit with protection and demand-based warm standby system.